ydx+x(lnx-lny-1)dy=0

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Solution for ydx+x(lnx-lny-1)dy=0 equation: 


Simplifying
ydx + x(lnx + -1lny + -1) * dy = 0

Reorder the terms:
dxy + x(-1 + lnx + -1lny) * dy = 0

Reorder the terms for easier multiplication:
dxy + x * dy(-1 + lnx + -1lny) = 0

Multiply x * dy
dxy + dxy(-1 + lnx + -1lny) = 0
dxy + (-1 * dxy + lnx * dxy + -1lny * dxy) = 0

Reorder the terms:
dxy + (-1dlnxy2 + dlnx2y + -1dxy) = 0
dxy + (-1dlnxy2 + dlnx2y + -1dxy) = 0

Reorder the terms:
-1dlnxy2 + dlnx2y + dxy + -1dxy = 0

Combine like terms: dxy + -1dxy = 0
-1dlnxy2 + dlnx2y + 0 = 0
-1dlnxy2 + dlnx2y = 0

Solving
-1dlnxy2 + dlnx2y = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'dlnxy'.
dlnxy(-1y + x) = 0


Subproblem 1
Set the factor 'dlnxy' equal to zero and attempt to solve:

Simplifying
dlnxy = 0

Solving
dlnxy = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
dlnxy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1y + x)' equal to zero and attempt to solve:

Simplifying
-1y + x = 0

Reorder the terms:
x + -1y = 0

Solving
x + -1y = 0

Move all terms containing d to the left, all other terms to the right.

Add '-1x' to each side of the equation.
x + -1x + -1y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -1y = 0 + -1x
-1y = 0 + -1x
Remove the zero:
-1y = -1x

Add 'y' to each side of the equation.
-1y + y = -1x + y

Combine like terms: -1y + y = 0
0 = -1x + y

Simplifying
0 = -1x + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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